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2 years ago

10

The growth of a population of mountain lions can be described by the function f(x) = 500(1.015)^x, where x is the number of year

s after the first census. How do the mathematical domain and range compare to the reasonable domain and range? Check all that apply. Thank you!

1 answer:

Arisa [49]2 years ago

6 0

Answer:

The mathematical and reasonable domains are identical

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X squared minus 7x plus 10 equals 0

joja [24]

X² - 7x + 10 = 0

Let's factor out the equation first.

x² - 7x + 10

x -2
x -5

This factoring of (x-2)(x-5) fit the equation.

(x-2)(x-5) = 0

One of the factors must equal 0 as to equal zero.

Either x - 2 = 0 or x - 5 = 0

x - 2 = 0
x = 2

x - 5 = 0
x = 5

The two answers are x = 2 or x = 5. Hope this helps!

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2 years ago

X + 4 is prime x2 – 9 can be factored using the formula.

Anna71 [15]

We are given two binomials: x+4 , x^2-9.

x+4 can't be factored. Therefore, it is a prime.

Let us work on x^2-9.

9 could be written as 3^2.

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Now, we can apply difference of the squares formula to factor it.

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One of the legs of a right triangle measures 9 cm and the other leg measures 11 cm.

ikadub [295]

Answer:

$\boxed {\boxed {\sf 14.2 \ cm}}$

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem to solve for the sides.

$a^2+b^2=c^2$

where <em>a</em> and<em> b</em> are the legs and <em>c</em> is the hypotenuse. In this triangle, we know the legs are 9 centimeters and 11 centimeters, or:

a= 9 cm
b= 11 cm

Substitute these values into the formula.

$(9 \ cm)^{2} +(11 \ cm)^{2} =c^{2}$

Solve the exponents.

(9 cm)²= 9 cm*9 cm=81 cm²

$81 \ cm^{2} +(11 \ cm)^{2} =c^{2}$

(11 cm)²= 11 cm*11 cm= 121 cm²

$81 \ cm^{2} +121 cm^{2} =c^{2}$

Add the values on the left side.

$202 \ cm^{2} =c^{2}$

Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.

$\sqrt {202 \ cm^{2} }=\sqrt{c^{2} }$

$\sqrt {202 \ cm^{2} }=c$

$14.2126704036 \ cm =c$

We are told to round to the nearest tenth.

14.2<u>1</u>26704036

The 1 in the hundredth place tells us to leave the 2 in the tenth place.

$14.2 \ cm= c$

The hypotenuse is equal to <u>14.2 centimeters.</u>

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